High order perturbative corrections to the determination of |V{sub ub}| from the P{sub +} spectrum in B{yields}X{sub u}l{nu}{sub l}
- Departament de Fisica Teorica and Instituto de Fisica Corpuscular, Universitat de Valencia-Consejo Superior de Investigaciones Cientificas, E-46100 Burjassot, Valencia (Spain)
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7 (Canada)
We investigate the behavior of the perturbative relation between the photon energy spectrum in B{yields}X{sub s}{gamma} and the hadronic P{sub +} spectrum in semileptonic B{yields}X{sub u}l{nu} decay at high orders in perturbation theory in the 'large-{beta}{sub 0}' limit, in which only terms of order {alpha}{sub s}{sup n}{beta}{sub 0}{sup n-1} are retained. The leading renormalon in the weight function W({delta},P{sub {gamma}}) relating the two spectra is confirmed to be at u=1/2, corresponding to nonperturbative corrections at O({lambda}{sub QCD}/m{sub b}). We show that the P{sub {gamma}} dependent pieces of the weight function have no infrared renormalons in this limit, and so the factorial growth in perturbation theory arises solely from the constant terms. We find no numerical enhancement of leading logarithms, suggesting that fixed-order perturbation theory is more appropriate than a leading-log resummation for the extraction of |V{sub ub}|. The importance of various terms in the expansion of the weight function is studied using a model for the B{yields}X{sub s}{gamma} photon spectrum. Our analysis suggests that higher order perturbative corrections do not introduce a significant uncertainty in the extraction of |V{sub ub}|.
- OSTI ID:
- 21308411
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 79, Issue 9; Other Information: DOI: 10.1103/PhysRevD.79.094007; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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